Fiscal Volatility Shocks and Economic Activity
Jesús Fernández-Villaverde, Pablo Guerrón Quintana,
Keith Kuester, Juan Rubio Ramírez
University of Pennsylvania
March 2, 2016
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Motivation: policymakers’ travails
I
From 2010 to 2013, many policymakers and observers saw the
U.S. economy as buffeted by larger-than-usual uncertainty about
fiscal policy.
I
There was little consensus among policymakers about the fiscal mix
and timing going forward.
Ben Bernanke [July 18, 2012]:
“The recovery in the United States continues to be held back by a
number of other headwinds, including still-tight borrowing conditions for
some businesses and households, and – as I will discuss in more detail
shortly – the restraining effects of fiscal policy and fiscal uncertainty.”
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Motivation: electoral history
I
8 patterns of party control at the Federal level (combination of
President-Senate-House).
I
The 6 elections between 2004 and 2014 have produced 5 out of
these 8 patterns.
I
Tie with 1878-1896 and 1910-1920 for the highest electoral
instability in U.S. history.
I
Ideological indexes suggest that the electoral instability of
1878-1896 and 1910-1920 had less severe consequences than
electoral instability now.
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Ideological position of members of Congress
(DW-Nominate)
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Objective
I
Quantify the effects of fiscal volatility shocks on economic activity.
I
We estimate tax and spending processes for the U.S. with
time-variant volatility using a Particle filter and a McMc.
I
We feed the estimated rules into an estimated equilibrium business
cycle model of the U.S. economy.
I
We simulate the equilibrium using a third-order perturbation (new
formulae for analytic non-linear IRFs).
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Main results I
1. We find a considerable amount of time-varying volatility in all four
fiscal instruments.
2. After a fiscal volatility shock, output, consumption, hours, and
investment drop on impact and stay low for several quarters.
Main transmission mechanism: an endogenous increase in
mark-ups.
Upward pricing bias due to the shape of the profit function.
3. Fiscal volatility shocks are “stagflationary": inflation goes up while
output falls.
4. We estimate a CEE-style VAR and an ACEL-style VAR to document
that, after a fiscal volatility shock, markups significantly increase.
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Why the “stagflation”?
I
Steady-state profits: Pj /P
1−
y − mc Pj /P
−
y
Period profits
0.05
0
−0.05
11
21
41
−0.1
−0.15
−0.2
0.95
1
1.05
relative price (Pj /P)
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Main results II
5. A two-standard deviations fiscal volatility shock has an effect similar
to a 30 b.p. innovation in the FFR as estimated by a SVAR.
6. At the ZLB, the effects are much bigger: 1.7 percent fall of output if
we are at the ZLB for 8 quarters.
7. Most important channel: larger uncertainty about the future tax rate
on capital income.
8. An accommodative monetary policy increases the effect of fiscal
volatility shocks.
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How do we quantify fiscal volatility shocks?
I
Volatility is not directly observed.
I
No data (surveys, asset prices...) or very limited (SPF for g, but
short horizon (5qtrs)).
I
Instead, we estimate a stochastic volatility process as in
Fernández-Villaverde et al. (2011).
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Empirical model
I
Fiscal instruments follow:
xt = ρx xt−1 + φx,y ỹt−1 + φx,b
bt−1
yt−1
+ exp(σx,t )εx,t
(1/2)
σx,t = (1 − ρσx ) σx + ρσx σx,t−1 + 1 − ρ2σx
ηx ux,t
I
x ∈ {g, τc , τl , τk }.
I
Fiscal shocks: εx,t .
I
Volatility shock: ux,t .
I
No direct effect on taxes.
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Data
I
Construct aggregate (average) effective tax rates from NIPA
(Mendoza et al., 1994; Leeper et al., 2010): consumption, labor and
capital income taxes.
I
General government (= federal + state + local).
I
Spending rule: ratio of government expenditures to GDP.
I
Federal debt (held by the public) from St. Louis Fed.
I
Data sample: 1970Q1 - 2010Q2.
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Estimation of fiscal rules
I
Instrument by instrument (easily extended).
I
No correlation of shocks (easily extended).
I
Particle filter+Bayesian methods.
I
Flat priors.
I
20,000 draws from posterior (5,000 additional burn-in draws) using
McMc.
I
10,000 particles to perform the evaluation of the likelihood.
Estimated Parameters
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Smoothed volatility: tax on capital income
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An age of uncertainty: 1973-1975, I
The Washington Post [September 16, 1973]:
“Is the Nixon administration inclined to favor a tax increase? The
authoritative answer last week was: (1) Yes; (2) No; (3) Maybe; (4) It is
under consideration."
I
Watergate scandal.
I
George Shultz resigns on May 8, 1974, substituted by William E.
Simon.
I
Richard Nixon resigns on August 9, 1974.
I
Evidence from Arthur Burns’ diary.
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An age of uncertainty: 1973-1975, II
The New York Times [January 15, 1975]:
“President Ford has not turned the economy around with his new energy
and economic proposals, but at least he has turned himself around."
I
Gerald Ford becomes president: Nixon’s pardon erodes his
credibility.
I
Constant fights between Nelson Rockefeller, Donald Rumsfeld, and
Dick Cheney.
I
Tax increase announced on October 8, 1974.
I
After ferocious infighting within the administration, a tax reduction
announced on January 16, 1975.
I
Continuous changes in Congress. Ford close to veto final tax cut.
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An age of uncertainty: 1973-1975, III
The Presidency of Gerald Ford [John Robert Greene]:
“The new mood in Capitol Hill made any kind of a coalition virtually
impossible even for such an experienced legislative hand as Gerald Ford.
More so than any other time since 1945, American government was truly
divided...."
I
Class of 1974 Congressman.
I
Breakdown of old committee system.
I
Wilbur Mills’ car stopped on October 9, 1974.
I
Al Ullman is less powerful.
I
Humphrey-Javits act about indicative planning.
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The Congressman and the Argentine Firecracker
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Forecast dispersion: tax on capital income
0.5
0.45
0.4
0.35
0.3
0.25
0
10
20
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30
40
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Relation with other measures of uncertainty
I
How much do we believe our empirical results?
I
Bloom et al. (2014) measure uncertainty using news media
coverage, tax provisions set to expire, and disagreement among
forecasters.
I
Surprisingly high correlation of their uncertainty measure with our
smoothed volatilities.
I
For instance, correlation of uncertainty with volatility of capital taxes:
0.56.
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Key ingredients
I
Representative household.
I
Labor supply flexible, but wages with quadratic adjustment cost.
I
Investment adjustment costs, but flexible utilization margin of capital.
I
Prices with quadratic adjustment cost.
I
Fiscal rules as discussed above+Taylor rule for monetary policy.
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Households I
I
Household maximizes:
(
Z 1 l 1+ϑ )
∞
1−ω
X
(c
−
b
c
)
j,t
t
h
t−1
−ψ
dj
E0
β t dt
1−ω
0 1+ϑ
t=0
I
Intertemporal shock dt :
log dt = ρd log dt−1 + σd εdt , εdt ∼ N (0, 1)
I
Savings:
1. Invest, it .
2. Hold government bonds, Bt , with nominal gross interest rate Rt .
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Households II
I
Budget constraint:
(1 + τc,t )ct + it + bt + Ωt +
1 − τl,t
R1
0
0
ACj,tw dj =
b +
wj,t lj,t dj + 1 − τk ,t rk ,t ut kt−1 + τk ,t δkt−1
+bt−1
I
R1
Rt−1
Πt
+ zt .
Real wage adjustment costs for labor type j:
ACj,tw =
φw
2
2
wj,t
− 1 yt
wj,t−1
I
Quadratic cost 6= Calvo. Remember: non-linear solution!
I
We also computed the model with Calvo pricing.
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Households III
I
Labor packer:
1
Z
lt =
w −1
w
lj,t
0
!
w
w −1
dj
I
Demand for each type of type of labor:
wj,t −w
lj,t =
lt
wt
I
By a zero-profit condition:
Z
wt =
0
FV-G-K-R
1
!
1−w
wj,t
1
1−w
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Households IV
I
Capital accumulation:
where:
I
it
it
kt = (1 − δ(ut )) kt−1 + 1 − S
it−1
1
δ(ut ) = δ + Φ1 (ut − 1) + Φ2 (ut − 1)2
2
Quadratic adjustment cost:
2
it
it
κ
S
=
−1
it−1
2 it−1
which implies S(1) = S 0 (1) = 0 and S 00 (1) = κ.
I
Book value of capital:
b
ktb = (1 − δ)kt−1
+ it
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Firms I
I
Competitive producer of a final good:
1
Z
yt =
ε−1
ε
yit
0
!
ε
ε−1
di
I
Buys intermediate goods at price Pi,t and charges Pt .
I
Demand:
yit =
I
Pit
Pt
−ε
yt
Price index:
Z
Pt =
0
FV-G-K-R
1
!
1
1−ε
Pit1−ε di
Fiscal Volatility
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Firms II
I
Intermediate good producer with market power:
yit = At kitα lit1−α − φ
I
At is neutral productivity:
log At = ρA log At−1 + σA εAt , εAt ∼ N (0, 1) and ρA ∈ [0, 1)
I
Intermediate producer sets prices at cost:
p
ACi,t
φp
=
2
FV-G-K-R
Pi,t
−Π
Pi,t−1
Fiscal Volatility
2
yi,t
26 / 45
Government
I
Monetary authority follows Taylor rule:
Rt
=
R
I
Rt−1
R
1−φR Πt
Π
(1−φR )γΠ yt
y
(1−φR )γy
eσm ξt
Fiscal authority’s budget constraint:
bt =
bt−1
Rt−1
Πt
b τ
+gt − ct τc,t + wt lt τl,t + rk ,t ut kt−1 τk ,t − δkt−1
k ,t + Ωt
I
Transfers:
Ωt = Ω + φΩ,b (bt−1 − b)
where φΩ,b > 0.
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Aggregation and solution
I
Aggregate demand:
φp
φw
yt = ct + it + gt +
(Πt − Π)2 yt +
2
2
I
2
wt
− 1 yt
wt−1
Aggregate supply:
yt = At (ut kt−1 )α lt1−α − φ
I
Market clearing.
I
Definition of equilibrium is standard.
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Estimation
I
General point: problems for calibration in non-linear models.
I
The Pruned State-Space System for Non-Linear DSGE Models:
Theory and Empirical Applications.
I
We use a SMM to estimate most parameters.
I
Parameters for fiscal instruments laws of motion: median of our
posteriors.
I
Third-order perturbation solution. Why?
I
Non-linear IRFs. Why?
Details of the Estimation
FV-G-K-R
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Experiment
xt = ρx xt−1 + φx,y ỹt−1 + φx,b
bt−1
yt−1
+ exp(σx,t )εx,t
(1/2)
σx,t = (1 − ρσx ) σx + ρσx σx,t−1 + 1 − ρ2σx
ηx ux,t
I
At time 0, the economy is hit by a fiscal volatility shock to capital
income tax.
I
Taxes are constant today.
I
Two-standard deviation shocks to uk ,t .
Meant to capture current fiscal outlook.
Perotti (2007), Bloom (2009).
FV-G-K-R
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Fiscal volatility shocks
output
cons.
invest.
hours
0
0
0
−0.5
−0.02
−0.05
−0.05
0
−1
−0.04
−0.1
10
−0.06
0
marg. cost
10
inflation (bps)
0
−0.06
0
10
0
0
10
0
nom. rate (bps)
10
wages
0
−0.02
20
20
−0.04
−1.5
0
40
40
−0.02
−0.1
−0.04
10
FV-G-K-R
0
0
−0.06
10
Fiscal Volatility
0
10
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Fiscal volatility shocks (black solid)
vs. 30bps monetary shock (red dots)
output
cons.
0.1
invest.
hours
0.5
0.05
0
0
−0.1
10
marg. cost
0
10
inflation (bps)
0
−0.02
−0.04
−0.06
0
10
40
20
0
−20
−40
0
0
−0.1
−1
−0.05
−0.2
0
0
−0.5
−1.5
0
−0.2
10
nom. rate (bps)
40
FV-G-K-R
10
wages
0.05
20
0
0
−0.05
−20
0
10
0
10
Fiscal Volatility
−0.1
0
10
32 / 45
VAR evidence:
IRFs
output
0.2
0
−0.2
−0.4
−0.6
0
consumption
investment
0
0
−0.2
−2
−0.4
5
10
quarters
15
−0.6
0
5
10
quarters
hours
15
−4
0
15
inflation (bps)
markup
0.3
0.5
5
10
quarters
0
0.2
0.1
0
−20
0
−0.5
0
5
10
quarters
15
−0.1
0
nominal rate (bps)
20
0
−20
−40
−60
−80
0
−40
5
10
quarters
15
real wage
30
−0.2
20
−0.4
10
15
0
−0.8
15
5
10
quarters
capital tax vola
0
−0.6
5
10
quarters
0
0
5
10
quarters
FV-G-K-R
−10
15
0
Fiscal Volatility
5
10
quarters
15
33 / 45
The effect of the ZLB
output
0.1
0
−0.1
−0.2
−0.3
0
−1
−2
0
10
marginal cost
0.4
0.2
0
−0.2
−0.4
−0.6
0
cons.
0
0
0
−1
−5
−2
−10
0
10
inflation (bps)
FV-G-K-R
0
10
wages
0.1
0
X: 1
Y: 0
0
10
10
nominal rate (bps)
800
600
400
200
0
−100
−150
0
hours
5
−50
10
invest.
−0.1
10
Fiscal Volatility
0
10
34 / 45
Monetary policy
output
cons.
invest.
hours
0
0
0
0
−1
−0.05
−0.1
−0.1
−2
−0.2
0
10
marg. cost
−0.1
0
10
inflation (bps)
0
0
10
nom. rate (bps)
10
wages
0
100
100
−0.05
−0.05
50
50
−0.1
−0.1
0
I Rt
R
−0.2
0
10
=
Rt−1
R
0
0
1−φR 0
0
10
Πt
Π
10
(1−φR )γΠ ↑=1.5 (1−φR )γy ↑=0.5
yt
y
FV-G-K-R
Fiscal Volatility
0
10
eσm ξt
35 / 45
Degree of nominal rigidities
output
consumption
investment
hours
0
0
−0.05
−0.1
0
−0.04
10
0
marginal cost
0
−0.2
−0.4
−0.6
−0.8
−1
−1.2
−0.02
10
−0.05
−0.1
0
inflation(bps)
10
0
nominal rate(bps)
0
10
wages
40
40
0
20
20
−0.05
−0.02
−0.04
−0.06
0
−0.08
0
I
I
I
10
0
0
0
10
10
−0.1
0
10
blue: (Calvo) φp = 0.1
red: (Calvo) φw = 0.1
magenta: (Calvo) φp = 0.1 and φw = 0.1
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The role of precautionary price setting
output
cons.
invest.
hours
0
0.05
0.05
−0.5
−0.02
0
−0.05
0
−0.05
−0.04
−1
−0.06
0
−1.5
0
−0.1
−0.1
0
10
marg. cost
infl.
40
−0.05
10
0
0
0
10
wages
0
−0.02
20
20
0
10
nom. rate
40
0.05
0
10
−0.04
10
FV-G-K-R
0
0
−0.06
10
Fiscal Volatility
0
10
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The future
I
So far, I have dealt with two-sided risk.
I
This may not capture what many observers have in mind: one-sided
risk. For instance, taxes will increase, but we do not know why how
much.
I
A simple alternative: innovation to shock+volatility shock.
I
A more appealing alternative: one-sided risk.
I
Formally: shocks to skewness.
I
One-Sided Risk and Economic Activity (2014).
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One-side risk
I
Stochastic process:
xt = ρxt−1 + (1 − ρ)υt
+ (1 − ρ2 )(1/2) eτt ωt + (1 − ρ)eαt ξt1 − (1 − ρ)eβt ξt2
where
υt = (1 − ρυ )υ + ρυ υt−1 + ηυ (1 − ρ2υ )(1/2) ε1t
τt = (1 − ρτ )τ + ρτ τt−1 + ητ (1 − ρ2τ )(1/2) ε2t
αt = (1 − ρα )α + ρα αt−1 + ηα (1 − ρ2α )(1/2) ε3t
βt = (1 − ρβ )β + ρβ βt−1 + ηβ (1 − ρ2β )(1/2) ε4t
ωt ∼ N (0, 1), ξti ∼ exp (1) , εjt ∼ N (0, 1)
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Conclusion
I
High fiscal volatility is a concern for policymakers.
I
But, how big are the effects of fiscal volatility shocks?
I
Our simulations indicate that the effect can be important.
I
Key role for monetary policy in propagation.
I
Modeling of political-economic equilibrium that leads to these shocks
remains an open issue.
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Estimated parameters
Tax rate on
Labor
ρx
σx
φx,y
φx,b
ρσx
ηx
Government
Consumption
Capital
Spending
0.99
0.99
0.97
0.97
[0.975,0.999]
[0.981,0.999]
[0.93,0.996]
[0.948,0.992]
−6.01
−7.09
−4.96
−6.13
[−6.27,−5.75]
[−7.34,−6.78]
[−5.29,−4.66]
[−6.49,−5.39]
0.031
0.001
0.044
−0.004
[0.011,0.055]
[0.000,0.005]
[0.004,0.109]
[−0.02,0.00]
0.003
0.0006
0.004
−0.008
[0.00,0.007]
[0.00,0.002]
[0.00,0.016]
[−0.012,−0.003]
0.31
0.65
0.76
0.93
[0.06,0.57]
[0.08,0.91]
[0.47,0.92]
[0.43,0.99]
0.94
0.60
0.57
0.43
[0.73,1.18]
[0.31,0.93]
[0.33,0.88]
[0.13,1.15]
Notes: The posterior median and a 95% probability interval.
I
Persistent mean-dynamics.
I
Stochastic volatility is significant and moderately persistent.
Return
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Estimation I
Preferences and consumer
β
0.9945
ω
2
Standard choice.
ϑ
2
Chetty (2011).
ψ
75.66
bh
0.75
CEE (JPE, 2005).
φw
4889
ACEL (RED, 2011).
21
ACEL (RED, 2011).
Estimated.
Estimated.
Cost of utilization and investment
Φ1
0.0165
From utilization FOC.
Φ2
0.0001
Estimated.
3
Estimated.
κ
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Estimation II
Firms
A
1
α
0.36
δ
0.011
φp
236.10
w
21
Normalization
Standard choice.
Estimated.
Gali and Gertler (JME, 1999).
ACEL (RED, 2011).
Monetary policy and lump-sum taxes
1.0045
Estimated.
φR
0.6
Estimated.
γΠ
1.25
FGR (2010).
γy
1/4
FGR (2010).
Ω
-4.3e-2
Follows from gov. budget constraint.
φΩ,b
0.0005
Small number to stabilize debt.
Π
b
2.64
Estimated.
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Estimated III
Shocks
I
ρA
0.95
King and Rebelo (1999).
σA
0.001
ρd
0.18
σd
0.078
Estimated.
σm
0.0001
Estimated.
Estimated.
Smets and Wouters (AER, 2007).
Parameters for fiscal instruments laws of motion: median of our
posteriors.
Return
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Decomposing fiscal volatility shocks
output
cons.
invest.
hours
0.02
0.2
0
−0.2
−0.4
−0.6
0
0
−0.1
−0.02
−0.2
0
10
20
0
marg. cost
10
20
inflation(bps)
40
−0.02
0
−0.1
0
10
20
nominal rate(bps)
10
20
wages
20
0
10
−0.01
20
0
−0.04
−0.06
0
−0.2
0
−0.02
0
10
20
−20
0
−10
10
20
0
10
20
−0.03
0
I
black: benchmark.
I
red: volatility shock only on capital income taxes.
FV-G-K-R
Fiscal Volatility
10
20
45 / 45